-8y + 25 ≤ -31
Please Answer

Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.

The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:

[tex]angle = arctan(rise/run)[/tex]

For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:

[tex]new rise = tan(angle) * new run[/tex]

[tex]new rise = tan(75.96) * 19[/tex]

new rise ≈ 18.7 feet

So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:

new rise = tan(angle) x new run

new rise = tan(75.96) x 22

new rise ≈ 21.3 feet

Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.

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Answer:

y= -1/4x+b

Step-by-step explanation:

see image

The statements which can be assumed from the diagram are:

Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross.

Parallel curves are curves that do not touch each other or intersect and preserve a predetermined minimum distance

In simple geometry, two geometric objects are perpendicular if the intersection at the point of junction known as a foot results in right angles.

From the given image, it can be seen that

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Answer:

C, E

Step-by-step explanation:

Answer choice A implies that [tex]42 +22 \geq 50 + 27[/tex], which is false

Answer choice B implies that 50 is half of the population, however the population is 200, so it is false

Answer choice C implies that [tex]50 + 27\geq[/tex] all other combinations, which is true.

Answer choice D implies that [tex]33 + 22\leq 50[/tex], which is false

Answer choice E implies that [tex]42 \leq 22+22[/tex], which is true

So, C & E are correct

Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.

On the x- axis the y- coordinate of any point is zero.

Set the factored form of the polynomial to zero and solve for x

x(x - 3)(x + 3)(x - 2) = 0

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

the x-intercepts are then x = - 3, x = 0, x = 2, x = 3

these can be confirmed from the graph of the polynomial

Triangle IJK is an isosceles triangle.

The slope of IJ is -2, the slope of JK is 1, and the slope of IK is 2. The length of IJ is 8, the length of JK is 4, and the length of IK is 6. Triangle IJK is an isosceles triangle.
√Correct

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The function that generates the sequence 1, 2, 4, 8, ... is:

Of(x) = 2^(x-1)

We can check this by plugging in the first few values of x:

Of(1) = 2^(1-1) = 1

Of(2) = 2^(2-1) = 2

Of(3) = 2^(3-1) = 4

Of(4) = 2^(4-1) = 8

Therefore, the answer is option B.

a. False
b. True
c. False
d. False

In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.

Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False

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The number of students who voted for each mascot is given as follows:

Then the difference is given as follows:

nT - nC.

The difference between the two amounts is obtained applying the proportions in the context of the problem.

The circle graph gives the percentage of each type of vote.

Hence the amounts relative to each type of vote are given as follows:

In which:

The problem is incomplete, hence the general procedure is given to solve the problem.

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Answer:

144

Step-by-step explanation:

The two variables that vary the most across these countries are "Animal Protein" and "Vegetable Protein."

The variable that varies the least is "Total Protein." The profile plot tells us that Denmark has the highest amount of animal protein, followed by Norway and then Sweden. However, Sweden has the highest amount of vegetable protein, followed by Denmark and then Norway. Overall, Denmark has the highest total protein, followed by Norway and then Sweden.

This suggests that Denmark relies more heavily on animal protein sources, while Sweden relies more heavily on vegetable protein sources. Norway falls somewhere in the middle, with a more balanced mix of animal and vegetable protein sources.

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The equation -7t-6=-7t has no solution.

Because when we try to isolate the variable t on one side of the equation, we end up with an equation that is not true.

Here's how we can do this:
-7t-6=-7t

First, we can add 7t to both sides of the equation:
-6=0

This equation is not true, so there are no values of t that will make this equation true. Therefore, the equation has no solution.

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Answer:

B

Step-by-step explanation:

The equivalent percent of 1/5 is 20%.  

To find this answer, we can convert the fraction to a decimal and then multiply by 100 to find the percent. Here are the steps:

1. Convert the fraction to a decimal: 1/5 = 0.2
2. Multiply the decimal by 100 to find the percent: 0.2 * 100 = 20%

Therefore, 1/5 is equivalent to 20%.

In terms of the shaded grid, if we were to shade 1 out of 5 squares, we would be shading 20% of the grid.

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The expressions that are equivalent to 2x - 3y = 12 are B and D.

We can modify the equation algebraically and simplify 2x - 3y = 12 to find the expressions that are equal to that number:

2x - 3y = 12

2x - 12 = 3y (subtract 12 from both sides) (subtract 12 from both sides)

(2/3)x - 4 = y (divide both sides by 3) (divide both sides by 3)

As a result, the equation can also be written as y = (2/3)x – 4.

We can now determine which expressions have the same meaning as this form:

A. y = 4 - (2/3)x

This expression is simplified to give y = (-2/3)x + 4. This isn't the same as y = (2/3)x – 4.

B. y = (2/3)x - 4

This formula already equals y = (2/3)x - 4 in terms of value.

C. 2x - 3y = -12

2x - 3y + 12 = 0 is the result of adding 12 to both sides of the equation. y = (2/3)x - 4 is not the same form as this.

D. y = (3/2)x - 6

This expression can be simplified to y = (2/3)x - 4 by doing so. The formula for this is y = (2/3)x – 4.

Hence, the formulas B and D are the same as 2x - 3y = 12.

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The probabilities, using the binomial distribution, are given as follows:

a. P(X = 2) = 0.2109.

b. P(X = 3) = 0.0469.

c. P(X ≥ 2) = 0.2617.

d. P(X < 3) = 0.9492.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given by the equation presented as follows:

The parameters, and their meaning are listed as follows:

The parameter values for this problem are given as follows:

n = 4, p = 0.25.

Hence the relevant probabilities are given as follows:

Then:

P(x ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2109 + 0.0469 + 0.0039 = 0.2617.

P(x < 3) = 1 - (P(X = 3) + P(X = 4)) = 1 - (0.0469 + 0.0039) = 0.9492.

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The simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

To simplify the expression (2x^(2)+5x+2)/(x^(2)+1x-6)-:(x^(2)+6x+8)/(2x^(2)-5x+2), we need to find a common denominator and then subtract the numerators. The common denominator in this case is (x^(2)+1x-6)*(2x^(2)-5x+2).

So, the expression becomes:

((2x^(2)+5x+2)*(2x^(2)-5x+2)-(x^(2)+6x+8)*(x^(2)+1x-6))/((x^(2)+1x-6)*(2x^(2)-5x+2))

Simplifying the numerator, we get:

(4x^(4)-5x^(3)-4x^(2)+27x+4-1x^(4)-7x^(3)-14x^(2)-6x-8x^(2)-48x-48)/((x^(2)+1x-6)*(2x^(2)-5x+2))

Combining like terms, we get:

(3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2))

So, the simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

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Step-by-step explanation:

Let L and W be the length and width of the rectangle, respectively.

We know that the perimeter, P, of a rectangle is given by:

P = 2L + 2W

In this case, P = 16 cm, so we have:

16 = 2L + 2W

Simplifying, we get:

8 = L + W

To find the greatest area of the rectangle, we need to maximize the product of L and W, which is the formula for the area, A:

A = L * W

We can solve for one variable in terms of the other using the equation we found earlier:

L = 8 - W

Substituting this into the formula for the area, we get:

A = (8 - W) * W

Expanding and simplifying, we get:

A = 8W - W^2

To find the maximum value of A, we can use calculus or complete the square. Completing the square, we get:

A = -(W - 4)^2 + 16

Since the square of a real number is always nonnegative, the maximum value of A occurs when (W - 4)^2 = 0, which is when W = 4.

Substituting this value back into the equation for the perimeter, we get:

8 = L + 4

L = 4

Therefore, the rectangle with a perimeter of 16 cm and the greatest area is a square with sides of length 4 cm, and its area is:

A = L * W = 4 * 4 = 16 square centimeters.

The equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) between two expressions, one on each side. An equation can contain variables, constants, numbers, and mathematical operations like addition, subtraction, multiplication, and division

To write an equation for the graph that passes through the points (4,-5) and (7,10), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line passing through the two points, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4,-5) and (x2, y2) = (7,10).

m = (10 - (-5)) / (7 - 4)

m = 15 / 3

m = 5

Now that we know the slope of the line, we can use either point to solve for the y-intercept, b. Let's use the point (4,-5):

y = mx + b

-5 = 5(4) + b

-5 = 20 + b

b = -25

Therefore, the equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

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Answer:₹14.40

Step-by-step explanation:

36x2=72

24x2=48

72+48=120x12=1440/100 =14.40

The exact length of segment AB is equal to: D. √13 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - 2)² + (5 - 2)²]

Distance = √[(2)² + (3)²]

Distance = √(4 + 9)

Distance = √13 units.

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The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).

Given the solutions;

To have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.

Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):

Hence;

(x + 3)(2x - 5)(x + 5i)(x - 5i)

Multiplying out these factors gives:

(x + 3)(2x - 5)(x + 5i)(x - 5i)

(x + 3)(2x - 5)(x² + 25)

= (2x² + x - 15)(x² + 25)

= 2x⁴ + x³ - 15x² + 50x² + 25x - 375

= 2x⁴ + x³ + 35x² + 25x - 375

So the polynomial in factored form is:

= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)

= 2(x + 3)(2x - 5)(x² + 25)

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Answer:

20000

Step-by-step explanation:

1.4 divided by 0.007%

1.4 - 0.0007%

x - 100%

0.0007x = 1.4

x = 2000

∴ 1.4 is 0.0007% of 2000.

The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.

To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:

Mass = Density x Volume

where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.

In the given question,

Using the given values, we can now calculate the mass of the solid copper cuboid in kg.

The volume of the copper cuboid is:

Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³

The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:

Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g

To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:

Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg

Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

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a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (1.96 for 95% confidence level)

p = proportion of beak adjustments estimated from preliminary investigation (0.3)

E = margin of error (0.1)

Plugging in the values:

n = (1.96^2 * 0.3 * 0.7) / 0.1^2

n = 38.15

Rounding up, we need at least 39 work sampling observations.

b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.

c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:

Standard = (Total time worked / Total number of beak adjustments) * 100

For the six employees summarized in the table:

Granny:

Standard = (82 / 164) * 100

Standard = 50 hours per hundred beak adjustments

Tweety:

Standard = (80 / 161) * 100

Standard = 49.69 hours per hundred beak adjustments

Item:

Standard = (200 / 185) * 100

Standard = 108.11 hours per hundred beak adjustments

Total:

Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100

Standard = 83.56 hours per hundred beak adjustments

The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:

Standard Error = Standard Deviation / √(n)

Where:

Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))

n = sample size

Using the data provided in the table, we can calculate the standard deviation and standard error as follows:

Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))

Standard Deviation = 55.88

Standard Error = 55.88 / √(6)

Standard Error = 22.83

This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

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The complete question goes thus:

ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99

The asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 .

To find the asymptotes of a rational function, we need to analyze the degree of the numerator and denominator, and find the values of x that make the denominator equal to zero.

First, let's find the vertical asymptotes. Vertical asymptotes occur when the denominator of a rational function is equal to zero. In this case, the denominator is 3x+6. Setting this equal to zero, we get:

3x+6=0
3x=-6
x=-2

So, the vertical asymptote is x=-2.

Next, let's find the horizontal asymptotes. Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 0 and the degree of the denominator is 1, so there is a horizontal asymptote. To find the horizontal asymptote, we need to look at the leading coefficients of the numerator and denominator. The leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 3. So, the horizontal asymptote is y=5/3.

Therefore, the asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 (vertical asymptote) and y=5/3 (horizontal asymptote).

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The sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

An assortment or set of potential results from a random experiment make up a sample space. With the letter "S," the sample space is denoted. Events are a subset of the possible results of an experiment. Depending on the experiment, a sample space could have several different outcomes. Discrete sample spaces, often known as finite sample spaces, are those that have a finite number of outcomes.

The sample space for choosing 1 card is given as:

Sample space = 8C1 = 8! / (1!)(8 - 1)!

Sample space = 8.

Hence, the sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

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To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.

The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:

1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)

Therefore, d/dx (csc(x)) = −csc(x)cot(x).

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The answer of another zero - polynomial function with real coefficient at 1+2i is 1-2i

The other zero of the polynomial function  with real coefficients and a zero at 1+2i is 1-2i.

This is because if a polynomial function with real coefficients has a complex zero,

then the conjugate of that zero is also a zero of the function. The conjugate of a complex number is obtained by changing the sign of the imaginary part.

Therefore, the conjugate of 1+2i is 1-2i. So, if 1+2i is a zero of the polynomial function, then 1-2i is also a zero of the function.

In summary, the other zero of the polynomial function with real coefficients and a zero at 1+2i is 1-2i.

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